CN-LEAGUE 2004 Problem 1

In an acute triangle $ABC$ , point $H$ is the intersection point of altitude $CE$ to $AB$ and altitude $BD$ to $AC$ . A circle with $DE$ as its diameter intersects $AB$ and $AC$ at $F$ and $G$ , respectively. $FG$ and $AH$ intersect at point $K$ . If $BC=25$ , $BD=20$ , and $BE=7$ , find the length of $AK$ .